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Analysis in Integer and Fractional Dimensions

Analysis in Integer and Fractional Dimensions Author Ron Blei
ISBN-10 1139427938
Release 2001-07-19
Pages
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This book provides a thorough and self-contained study of interdependence and complexity in settings of functional analysis, harmonic analysis and stochastic analysis. It focuses on 'dimension' as a basic counter of degrees of freedom, leading to precise relations between combinatorial measurements and various indices originating from the classical inequalities of Khintchin, Littlewood and Grothendieck. The basic concepts of fractional Cartesian products and combinatorial dimension are introduced and linked to scales calibrated by harmonic-analytic and stochastic measurements. Topics include the (two-dimensional) Grothendieck inequality and its extensions to higher dimensions, stochastic models of Brownian motion, degrees of randomness and Frechet measures in stochastic analysis. This book is primarily aimed at graduate students specialising in harmonic analysis, functional analysis or probability theory. It contains many exercises and is suitable to be used as a textbook. It is also of interest to scientists from other disciplines, including computer scientists, physicists, statisticians, biologists and economists.



The Grothendieck Inequality Revisited

The Grothendieck Inequality Revisited Author Ron Blei
ISBN-10 9780821898550
Release 2014-09-29
Pages 90
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The classical Grothendieck inequality is viewed as a statement about representations of functions of two variables over discrete domains by integrals of two-fold products of functions of one variable. An analogous statement is proved, concerning continuous functions of two variables over general topological domains. The main result is the construction of a continuous map $\Phi$ from $l^2(A)$ into $L^2(\Omega_A, \mathbb{P}_A)$, where $A$ is a set, $\Omega_A = \{-1,1\}^A$, and $\mathbb{P}_A$ is the uniform probability measure on $\Omega_A$.



Recent Trends in Orthogonal Polynomials and Approximation Theory

Recent Trends in Orthogonal Polynomials and Approximation Theory Author Guillermo Lopez Lagomasino
ISBN-10 9780821848036
Release 2010
Pages 298
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This volume contains invited lectures and selected contributions from the International Workshop on Orthogonal Polynomials and Approximation Theory, held at Universidad Carlos III de Madrid on September 8-12, 2008, and which honored Guillermo Lopez Lagomasino on his 60th birthday. This book presents the state of the art in the theory of Orthogonal Polynomials and Rational Approximation with a special emphasis on their applications in random matrices, integrable systems, and numerical quadrature. New results and methods are presented in the papers as well as a careful choice of open problems, which can foster interest in research in these mathematical areas. This volume also includes a brief account of the scientific contributions by Guillermo Lopez Lagomasino.



Normal Approximations with Malliavin Calculus

Normal Approximations with Malliavin Calculus Author Ivan Nourdin
ISBN-10 9781107017771
Release 2012-05-10
Pages 239
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Higher Moments of Banach Space Valued Random Variables

Higher Moments of Banach Space Valued Random Variables Author Svante Janson
ISBN-10 9781470414658
Release 2015-10-27
Pages 110
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The authors define the :th moment of a Banach space valued random variable as the expectation of its :th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. The authors study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals.



Mathematical Reviews

Mathematical Reviews Author
ISBN-10 UVA:X006180726
Release 2004
Pages
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Mathematical Reviews has been writing in one form or another for most of life. You can find so many inspiration from Mathematical Reviews also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Mathematical Reviews book for free.



Forthcoming Books

Forthcoming Books Author Rose Arny
ISBN-10 UOM:39015046820406
Release 2001-08
Pages
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Forthcoming Books has been writing in one form or another for most of life. You can find so many inspiration from Forthcoming Books also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Forthcoming Books book for free.



An Introduction to Lie Groups and Lie Algebras

An Introduction to Lie Groups and Lie Algebras Author Alexander Kirillov
ISBN-10 9780521889698
Release 2008-07-31
Pages 222
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This book is an introduction to semisimple Lie algebras; concise and informal, with numerous exercises and examples.



American Book Publishing Record

American Book Publishing Record Author
ISBN-10 STANFORD:36105111052903
Release 2002
Pages
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American Book Publishing Record has been writing in one form or another for most of life. You can find so many inspiration from American Book Publishing Record also informative, and entertaining. Click DOWNLOAD or Read Online button to get full American Book Publishing Record book for free.



Foundations of Ergodic Theory

Foundations of Ergodic Theory Author Marcelo Viana
ISBN-10 9781107126961
Release 2016-02-12
Pages 625
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Self-contained introductory textbook suitable for a variety of one- or two-semester courses. Rich with examples, applications and exercises.



Fourier Analysis and Hausdorff Dimension

Fourier Analysis and Hausdorff Dimension Author Pertti Mattila
ISBN-10 9781107107359
Release 2015-07-22
Pages 452
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Modern text examining the interplay between measure theory and Fourier analysis.



Introduction to Foliations and Lie Groupoids

Introduction to Foliations and Lie Groupoids Author I. Moerdijk
ISBN-10 1139438980
Release 2003-09-18
Pages
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This book gives a quick introduction to the theory of foliations, Lie groupoids and Lie algebroids. An important feature is the emphasis on the interplay between these concepts: Lie groupoids form an indispensable tool to study the transverse structure of foliations as well as their noncommutative geometry, while the theory of foliations has immediate applications to the Lie theory of groupoids and their infinitesimal algebroids. The book starts with a detailed presentation of the main classical theorems in the theory of foliations then proceeds to Molino's theory, Lie groupoids, constructing the holonomy groupoid of a foliation and finally Lie algebroids. Among other things, the authors discuss to what extent Lie's theory for Lie groups and Lie algebras holds in the more general context of groupoids and algebroids. Based on the authors' extensive teaching experience, this book contains numerous examples and exercises making it ideal for graduate students and their instructors.



Calculus of Variations

Calculus of Variations Author Jürgen Jost
ISBN-10 0521642035
Release 1998
Pages 323
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This textbook on the calculus of variations covers from the basics to the modern aspects of the theory.



Mathematics of Genome Analysis

Mathematics of Genome Analysis Author Jerome K. Percus
ISBN-10 0521585260
Release 2002
Pages 139
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The massive research effort known as the Human Genome Project is an attempt to record the sequence of the three trillion nucleotides that make up the human genome and to identify individual genes within this sequence. While the basic effort is of course a biological one, the description and classification of sequences also lend themselves naturally to mathematical and statistical modeling. This short textbook on the mathematics of genome analysis presents a brief description of several ways in which mathematics and statistics are being used in genome analysis and sequencing. It will be of interest not only to students but also to professional mathematicians curious about the subject.



Locally Convex Spaces over Non Archimedean Valued Fields

Locally Convex Spaces over Non Archimedean Valued Fields Author C. Perez-Garcia
ISBN-10 0521192439
Release 2010-01-07
Pages 486
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Non-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers are fundamental, is a fast-growing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry. This book is the first to provide a comprehensive treatment of non-Archimedean locally convex spaces. The authors provide a clear exposition of the basic theory, together with complete proofs and new results from the latest research. A guide to the many illustrative examples provided, end-of-chapter notes and glossary of terms all make this book easily accessible to beginners at the graduate level, as well as specialists from a variety of disciplines.



Random Walk and the Heat Equation

Random Walk and the Heat Equation Author Gregory F. Lawler
ISBN-10 9780821848296
Release 2010-11-22
Pages 156
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The heat equation can be derived by averaging over a very large number of particles. Traditionally, the resulting PDE is studied as a deterministic equation, an approach that has brought many significant results and a deep understanding of the equation and its solutions. By studying the heat equation and considering the individual random particles, however, one gains further intuition into the problem. While this is now standard for many researchers, this approach is generally not presented at the undergraduate level. In this book, Lawler introduces the heat equations and the closely related notion of harmonic functions from a probabilistic perspective. The theme of the first two chapters of the book is the relationship between random walks and the heat equation. This first chapter discusses the discrete case, random walk and the heat equation on the integer lattice; and the second chapter discusses the continuous case, Brownian motion and the usual heat equation. Relationships are shown between the two. For example, solving the heat equation in the discrete setting becomes a problem of diagonalization of symmetric matrices, which becomes a problem in Fourier series in the continuous case. Random walk and Brownian motion are introduced and developed from first principles. The latter two chapters discuss different topics: martingales and fractal dimension, with the chapters tied together by one example, a random Cantor set. The idea of this book is to merge probabilistic and deterministic approaches to heat flow. It is also intended as a bridge from undergraduate analysis to graduate and research perspectives. The book is suitable for advanced undergraduates, particularly those considering graduate work in mathematics or related areas.



L vy Processes and Stochastic Calculus

L  vy Processes and Stochastic Calculus Author David Applebaum
ISBN-10 9780521738651
Release 2009-04-30
Pages 460
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A fully revised and appended edition of this unique volume, which develops together these two important subjects.